An Extended Domain Method for Optimal Boundary Control for Navier-Stokes Equations

Abstract

The matching velocity problem for the steady-state Navier-Stokes system is considered. We introduce an extended domain method for solving optimal boundary control problems. The Lagrangian multiplier method is applied to the extended domain with distributed controls and used to determine the optimality system and the control over the boundary of the inner domain. The existence, the differentiability and the optimality system of the control problem are discussed. With this method inflow controls are shown to be numerical reliable over a large admissible control set. Numerical tests for steady-state solutions are presented to prove the effectiveness and robustness of the method for flow matching.